Recently, domestic market participants have a growing interest in synthetic Collateralized Debt Obligation (CDO) as a security to reduce credit risk and create new profit. Therefore, the valuation method and hedging strategy for synthetic CDO become an important issue. However, there is no won-denominated credit default swap transactions, which are essential for activating synthetic CDO transaction‘ In addition, there is no transparent market information for the default probability, asset correlation, and recovery rate, which are critical variables determining the price of synthetic CDO.
This study first investigates the method of estimating the default probability, asset correlation coefficient, and recovery rate. Next, using five synthetiC CDO pricing models‘ widely used OFGC (One-Factor Non-Gaussian Copula) model. OFNGC (One-Factor Non-Gaussian Copula) model such as OFDTC (One-Factor Double T-distribution Copula) model of Hull and White (2004) or NIGC (Normal Inverse Gaussian Copula) model of Kalemanova et al.(2005), SC<Stochastic Correlation) model of Burtschell et al.(2005), and FL (Forward Loss) model of Bennani (2005), I Investigate and compare three points: 1) appropriateness for portfolio loss distribution, 2) explanation for standardized tranche spread, 3) sensitivity for delta-neutral hedging strategy. To compare pricing models, parameter estimation for each model is preceded by using the term structure of iTraxx Europe index spread and the tranch spreads with different maturities and exercise prices Remarkable results of this study are as follows. First, the probability for loss interval determining mezzanine tranche spread is lower in all models except SC model than OFGC model. This result shows that all mαdels except SC model in some degree solve the implied correlation smile phenomenon, where the correlation coefficient of mezzanine tranche must be lower than other tranches when OFGC model is used. Second, in explaining standardized tranche spread, NIGC model is the best among various models with respect to relative error. When OFGC model is compared with OFDTC model, OFOTC model is better than OFGC model in explaining 5-year tranche spreads. But for 7-year or 10-year tranches, OFDTC model is better with respect to absolute error while OFGC model is better with respect to relative error. Third, the sensitivity sign of senior tranctle spread with respect to asset correlation is sometime negative in NIG model while it is positive in other models. This result implies that a long position may be taken by the issuers of synthet.ic COO as a correlation delta-neutral hedging strategy when OFGC model is used, while a short position may be taken when NIGC model is used.
A fully pipelined probability density function engine for Gaussian Copula model
